Chapter-wise PYQ
Class 12 Physics

State Gauss's law in electrostatics. Using Gauss's law, derive an expression for the electric field intensity due to a uniformly charged infinite plane sheet.

Define electric flux. Write its SI unit. Is it a scalar or vector quantity?

Two point charges +q and −q are placed at a distance d apart. Draw the electric field lines for this system.

An electric dipole of dipole moment p is placed in a uniform electric field E. Write the expression for the torque experienced by the dipole. In which orientation will the dipole be in stable equilibrium?

Derive the expression for the electric field intensity at a point on the axial line of an electric dipole.

Using Gauss's law, derive the expression for the electric field due to a uniformly charged thin spherical shell at a point (i) outside the shell and (ii) inside the shell.

A charge q is placed at the centre of a cube of side l. What is the electric flux through each face of the cube?

Explain the concept of electric field lines. State any four properties of electric field lines.

Derive an expression for the potential energy of a system of two point charges in the absence of any external electric field.

A parallel plate capacitor with air between the plates has a capacitance of 8 pF. What will be the capacitance if the distance between the plates is reduced to half and the space between them is filled with a substance of dielectric constant 6?

Define equipotential surface. Draw equipotential surfaces for (i) a uniform electric field and (ii) a point charge.

Derive an expression for the energy stored in a parallel plate capacitor. What is the energy stored in it when the capacitance is C, charge is Q and potential difference is V?

Explain why the electric potential at any point due to a dipole on its equatorial line is zero.

A 4 µF capacitor is charged by a 200 V supply. The supply is then disconnected and the charged capacitor is connected to another uncharged 2 µF capacitor. How much electrostatic energy of the first capacitor is lost?

Define the dielectric constant of a medium. What is its value for a conductor?

State Kirchhoff's laws of electrical networks. Apply Kirchhoff's laws to a balanced Wheatstone bridge and derive the condition for balance.

Define the term 'resistivity' of a conductor. Write its SI unit. How does the resistivity of a metallic conductor vary with temperature?

In a potentiometer experiment, the balancing length for a cell is 560 cm. When an external resistance of 10 Ω is connected across the cell, the balancing length changes to 490 cm. Find the internal resistance of the cell.

A battery of EMF ε and internal resistance r is connected to an external resistance R. Derive an expression for the current through the circuit and the terminal voltage of the battery.

Explain with a circuit diagram the working of a meter bridge to determine the unknown resistance of a wire.

State Ohm's law. Under what conditions does a conductor obey Ohm's law?

Two resistances, when connected in series, give equivalent resistance 16 Ω and when in parallel give 3 Ω. Find the individual resistances.

Define mobility of electrons in a conductor. Write the relation between drift velocity and electric field applied.

State Biot-Savart law. Using it, derive an expression for the magnetic field at the centre of a circular current-carrying loop.

Derive an expression for the force per unit length between two long, straight, parallel conductors carrying currents in the same direction. Hence define 1 Ampere.

A straight wire carrying a current of 12 A is bent into a semicircular arc of radius 2 cm. What is the magnetic field at the centre?

State Ampere's circuital law. Use it to obtain an expression for the magnetic field inside a toroid.

A charged particle moving with velocity v enters a magnetic field B at right angles to it. Derive an expression for the radius of the circular path described by the particle.

Explain the working principle of a moving coil galvanometer. How is it converted into (i) an ammeter and (ii) a voltmeter?

Write the expression for the magnetic field at the centre of a square coil of N turns, side length l, carrying current I.

Distinguish between diamagnetic, paramagnetic, and ferromagnetic substances. Give one example of each.

What is meant by magnetic susceptibility? How does it differ for diamagnetic and paramagnetic substances?

A bar magnet of magnetic moment M is placed in a uniform magnetic field B. Write the expressions for (i) maximum torque and (ii) potential energy when the dipole is aligned parallel to the field.

Explain the terms: (i) retentivity and (ii) coercivity with reference to a ferromagnetic material. What do these properties decide about its use?

State Faraday's laws of electromagnetic induction. Write the mathematical expression. State Lenz's law and explain how it is consistent with conservation of energy.

Derive an expression for the self-inductance of a long solenoid of N turns, length l, and cross-sectional area A.

A rectangular coil of area A and N turns is rotated with angular frequency ω in a uniform magnetic field B. Derive an expression for the EMF induced in the coil as a function of time.

Define mutual inductance. Write its SI unit. What is the mutual inductance of two concentric coils of radii r₁ and r₂ (r₂ >> r₁)?

A coil of resistance 40 Ω is connected to a galvanometer. When the flux through the coil changes from 0.1 Wb to 0.5 Wb in 0.1 s, find the charge that flows through the galvanometer.

Draw a labelled diagram of an AC generator. Derive an expression for the instantaneous value of the EMF induced. Define peak value and RMS value of the EMF.

An AC source of EMF E = E₀ sin ωt is connected to a series LCR circuit. Derive an expression for the impedance of the circuit. Write the condition for resonance.

Define power factor of an AC circuit. For which circuit element is the power factor zero, and for which is it one?

A 100 Ω resistor, 0.5 H inductor, and 25 µF capacitor are connected in series to a 220 V, 50 Hz AC supply. Find (i) impedance of the circuit and (ii) the RMS current.

Explain the principle and working of a transformer. Why is AC preferred over DC for long-distance power transmission?

Name the electromagnetic waves that have wavelengths in the range of (i) 10⁻² m to 10⁻³ m (ii) 10⁻¹⁰ m to 10⁻⁸ m. Write one use of each.

What are electromagnetic waves? How were they predicted by Maxwell? Write any two properties of electromagnetic waves.

Identify the electromagnetic waves whose wavelengths lie in the ranges: UV, infrared, microwave, gamma rays. Arrange them in increasing order of frequency.

Derive the lens maker's formula for a thin convex lens. Under what conditions does a convex lens act as a diverging lens?

Draw a ray diagram to show image formation by a concave mirror when an object is placed between the centre of curvature and the focus. State the nature and position of the image.

A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 30 cm. Find the power and focal length of the combination.

Define total internal reflection. State the conditions necessary for it. Write two applications of optical fibre based on total internal reflection.

Draw a labelled ray diagram of an astronomical telescope in the normal adjustment position. Write the expression for its magnifying power.

Using the mirror formula, show that a convex mirror always forms a virtual, erect, and diminished image of an object placed in front of it.

Derive Snell's law of refraction using Huygens' wave theory.

In Young's double slit experiment, derive the expression for fringe width. What happens to the fringe width if (i) the slit separation is doubled (ii) the screen is moved closer?

Distinguish between interference and diffraction of light.

In a single slit diffraction experiment, the width of the slit is 0.3 mm and the screen is 1.5 m away. If the wavelength of light is 589 nm, find the width of the central maximum.

State Huygens' principle. Using it, prove the law of reflection.

What is polarisation of light? How is plane-polarised light produced using a Polaroid? State Malus's law.

State Einstein's photoelectric equation. Explain how it accounts for (i) the existence of threshold frequency and (ii) the independence of maximum kinetic energy from intensity.

The work function of caesium is 2.14 eV. Find the threshold wavelength and the maximum kinetic energy of electrons emitted when light of wavelength 300 nm falls on the metal.

What is de Broglie wavelength? Derive the expression for the de Broglie wavelength of an electron accelerated through a potential difference V.

Draw a graph showing the variation of stopping potential with the frequency of incident radiation in the photoelectric effect. What does the slope of the graph represent?

State Bohr's postulates for hydrogen atom. Derive an expression for the radius of the nth orbit and the energy of the electron in the nth orbit.

Explain with a diagram: (i) Rutherford's scattering experiment and (ii) the conclusions drawn from it.

Using Bohr's postulates, derive an expression for the wavelength of radiation emitted when an electron in a hydrogen atom transitions from a higher energy level n₂ to a lower energy level n₁.

The ground state energy of hydrogen atom is −13.6 eV. Find the kinetic and potential energy of the electron in the third excited state.

Define binding energy per nucleon. Draw a graph of binding energy per nucleon vs mass number A. Use it to explain why nuclear fission and fusion both release energy.

Derive the law of radioactive decay. Define half-life and mean life of a radioactive nucleus. Write the relation between them.

The half-life of a radioactive element is 5 years. Calculate the activity of 1 g of the element if its atomic mass is 226. (Avogadro number = 6.023 × 10²³)

Distinguish between nuclear fission and nuclear fusion. Under what conditions can nuclear fusion occur?

Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and draw the output waveform.

With the help of a circuit diagram, explain how a transistor can be used as a switch.

Explain the formation of energy bands in solids. On this basis, distinguish between conductors, semiconductors, and insulators.

Draw the truth table and logic symbol for (i) NAND gate and (ii) NOR gate. Show that NAND gate is a universal gate.

Define the terms: (i) p-type semiconductor and (ii) n-type semiconductor. Draw the energy band diagrams for each.

A transistor is used in common emitter configuration. If the collector current changes by 2 mA for a base current change of 20 µA, find the current amplification factor β.